The solution method consists in the following. With each body we couple a local coordinate system within which the electromagnetic field is represented by the amplitudes of impressed-current waves and by unknown wave amplitudes determined by the presence of another body. We use the boundary conditions at the surface of each body in the local coordinate system to form an incomplete system of infinite linear equations in the unknown wave amplitudes. The wave-amplitude transformations complete this system of equations for transition from one local system to another. Solution of this system by the truncation method provides the solution to our problem.